Fuzzy stability of a cubic-quartic functional equation: a fixed point approach

Sun-Young Jang; Choonkil Park; Dong Yun Shin

doi:10.4134/BKMS.2011.48.3.491

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Bull. Korean Math. Soc. 2011; 48(3): 491-503

Printed May 1, 2011

https://doi.org/10.4134/BKMS.2011.48.3.491

Fuzzy stability of a cubic-quartic functional equation: a fixed point approach

Sun-Young Jang, Choonkil Park, and Dong Yun Shin

University of Ulsan, Hanyang University, University of Seoul

Abstract

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Abstract

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quartic functional equation \begin{align} f(2x+y) + f(2x-y) = &\ 3f(x+y) + f(-x-y) + 3 f(x-y) + f(y-x) \\ &\ + 18f(x) + 6f(-x) - 3f(y) - 3f(-y) \notag \end{align} in fuzzy Banach spaces.

Keywords: fuzzy Banach space, fixed point, generalized Hyers-Ulam stability, quartic mapping, cubic mapping

MSC numbers: Primary 46S40, 39B72; Secondary 39B52, 46S50, 26E50, 47H10